<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:creator>Belius, David</dc:creator>
  <dc:creator>Concetti, Francesco</dc:creator>
  <dc:creator>Genovese, Giuseppe</dc:creator>
  <dc:date>2025</dc:date>
  <dc:description xmlns:ns0="xml" ns0:lang="en">We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on $\R$. The formula is given in terms of the $R$-transform of the first measure, and the logarithmic potential of second measure. The result applies in particular to the additive convolution with the semicircle or Marchenko-Pastur laws, for which the formula simplifies. The logarithmic potential of additive convolutions appears for instance in estimates of the determinant of sums of independent random matrices.</dc:description>
  <dc:format>application/pdf</dc:format>
  <dc:identifier>https://n2t.net/ark:/51647/srd1336037</dc:identifier>
  <dc:identifier>https://sonar.unidistance.ch/global/documents/336037</dc:identifier>
  <dc:identifier>https://sonar.unidistance.ch/documents/336037/files/Variational-formula-for-the-logarithmic-potential-of-free-additive-convolutions.pdf</dc:identifier>
  <dc:relation>info:eu-repo/semantics/altIdentifier/doi/10.48550/ARXIV.2506.19064</dc:relation>
  <dc:relation>info:eu-repo/semantics/altIdentifier/ark/51647/srd1336037</dc:relation>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:title xmlns:ns1="xml" ns1:lang="en">Variational formula for the logarithmic potential of free additive convolutions</dc:title>
  <dc:type>http://purl.org/coar/resource_type/c_816b</dc:type>
</oai_dc:dc>